1 00:00:01,096 --> 00:00:02,836 - [Voiceover] Young's Double Slit experiment 2 00:00:02,836 --> 00:00:04,324 looked a little something like this. 3 00:00:04,324 --> 00:00:06,307 You've got a barrier with two holes in it, 4 00:00:06,307 --> 00:00:09,601 but these holes are so small and so close together 5 00:00:09,601 --> 00:00:12,291 we characterize them as slits, 6 00:00:12,291 --> 00:00:14,309 and double because there's two of them. 7 00:00:14,309 --> 00:00:16,085 Young was the English physicist who first 8 00:00:16,085 --> 00:00:17,770 did an experiment of this kind. 9 00:00:17,770 --> 00:00:19,851 What we do nowadays is we take a laser, 10 00:00:19,851 --> 00:00:22,520 and we shine this laser at the double slit. 11 00:00:23,107 --> 00:00:27,790 The laser has to be wide enough that it hits both holes. 12 00:00:27,790 --> 00:00:29,711 You might think, oh my god, you need a big laser. 13 00:00:29,711 --> 00:00:31,709 No, you make these holes very close together. 14 00:00:31,709 --> 00:00:33,392 That's why you make them really close together, 15 00:00:33,392 --> 00:00:35,051 or at least one reason. 16 00:00:35,051 --> 00:00:37,151 The other reason is the distance between 17 00:00:37,151 --> 00:00:39,453 these holes has to be comparable. 18 00:00:39,887 --> 00:00:41,532 It doesn't have to be the same size or smaller, 19 00:00:41,532 --> 00:00:42,977 but it has to be around. 20 00:00:42,977 --> 00:00:44,930 It can't be a trillion times bigger 21 00:00:44,930 --> 00:00:47,276 than the wavelength of this laser light 22 00:00:47,276 --> 00:00:48,185 you're sending in here. 23 00:00:48,185 --> 00:00:49,257 It's got to be around the same size, 24 00:00:49,257 --> 00:00:52,360 or what we're going to talk about here you won't see. 25 00:00:52,360 --> 00:00:53,531 You won't see the interesting pattern 26 00:00:53,531 --> 00:00:54,517 that's going to emerge. 27 00:00:54,517 --> 00:00:55,835 You might wonder I've drawn here. 28 00:00:55,835 --> 00:00:56,925 What is this? 29 00:00:57,325 --> 00:00:58,565 This isn't a wave. 30 00:00:58,825 --> 00:01:00,536 This is a wave, right here. 31 00:01:00,536 --> 00:01:01,785 I thought these were waves. 32 00:01:01,785 --> 00:01:02,661 What are we doing now? 33 00:01:02,661 --> 00:01:04,241 Why have we got this different representation? 34 00:01:04,241 --> 00:01:06,116 The reason is, when I draw this, 35 00:01:06,116 --> 00:01:09,353 this pretty much just lets me show a wave in one dimension. 36 00:01:09,814 --> 00:01:10,722 But that's not good enough. 37 00:01:10,722 --> 00:01:13,689 This process is going to be fundamentally two-dimensional. 38 00:01:13,689 --> 00:01:15,661 This wave's going to spread out in two dimensions, 39 00:01:15,661 --> 00:01:17,268 so I can't draw it like this, 40 00:01:17,268 --> 00:01:18,164 I have to draw it like this. 41 00:01:18,164 --> 00:01:19,979 This whole line here, what does this represent? 42 00:01:19,979 --> 00:01:21,626 This represents a peak. 43 00:01:21,626 --> 00:01:23,496 Everywhere along here is a peak of the wave, 44 00:01:23,496 --> 00:01:26,763 so you've got this wave filling up this entire region. 45 00:01:26,763 --> 00:01:29,736 These lines represent lines where every point 46 00:01:29,736 --> 00:01:31,756 along there is a peak of the wave. 47 00:01:31,756 --> 00:01:32,580 What's in the middle? Yup. 48 00:01:32,580 --> 00:01:34,997 In the middle would be the trough of the wave, 49 00:01:34,997 --> 00:01:36,282 or the valley. 50 00:01:36,282 --> 00:01:37,559 That's what I'm going to use. 51 00:01:37,559 --> 00:01:39,667 I'm going to use this representation for the wave. 52 00:01:39,667 --> 00:01:41,631 This will let me show this wave spreading 53 00:01:41,631 --> 00:01:44,542 out in two dimensions better than this one could. 54 00:01:44,542 --> 00:01:46,099 I couldn't draw it very well with this one. 55 00:01:46,099 --> 00:01:47,700 So, what happens? 56 00:01:47,700 --> 00:01:50,582 This wave comes in here, this laser light comes in here. 57 00:01:50,582 --> 00:01:53,219 That part hits that barrier, it doesn't get through. 58 00:01:53,219 --> 00:01:54,802 This part hits that barrier, it doesn't get through. 59 00:01:54,802 --> 00:01:56,769 This part hits the barrier, it doesn't get through. 60 00:01:56,769 --> 00:01:58,046 The only portion that's going to get through 61 00:01:58,046 --> 00:02:02,168 is basically this portion here and this portion here. 62 00:02:02,168 --> 00:02:04,880 These are going to be the ones that make it through. 63 00:02:04,880 --> 00:02:05,927 What happens? 64 00:02:05,927 --> 00:02:07,673 What do you see on the wall over here? 65 00:02:07,673 --> 00:02:09,252 If this was a screen that you could project 66 00:02:09,252 --> 00:02:11,710 the light on, what would you see? 67 00:02:11,710 --> 00:02:13,558 Naively, what I would have thought would have been, 68 00:02:13,558 --> 00:02:16,255 okay, shoot, light comes through here, bright spot. 69 00:02:16,255 --> 00:02:18,659 Light comes through here, bright spot. 70 00:02:18,659 --> 00:02:20,468 You just get two bright spots, right? 71 00:02:20,468 --> 00:02:21,745 Well, no, that's not what you get. 72 00:02:21,745 --> 00:02:23,697 That's why this experiment is interesting, 73 00:02:23,697 --> 00:02:26,146 because you don't just get two bright spots. 74 00:02:26,146 --> 00:02:27,841 You get a pattern over here, 75 00:02:27,841 --> 00:02:31,625 because waves don't just travel straight through this hole. 76 00:02:31,625 --> 00:02:34,440 When a wave encounters a hole or a corner, 77 00:02:34,440 --> 00:02:35,444 it spreads out. 78 00:02:35,444 --> 00:02:38,837 That spreading out we call diffraction. 79 00:02:38,837 --> 00:02:41,102 You're going to get a wave spreading out from down here. 80 00:02:41,102 --> 00:02:42,660 This is not going to go in a straight line. 81 00:02:42,660 --> 00:02:44,385 It spreads out in two dimensions. 82 00:02:44,385 --> 00:02:47,647 That's why I had to use this wave drawing representation. 83 00:02:47,647 --> 00:02:49,683 It's going to spread out from the top one, too. 84 00:02:49,683 --> 00:02:51,263 Uh-oh, look what's going to happen. 85 00:02:51,263 --> 00:02:53,478 You're going to have two waves overlapping. 86 00:02:53,478 --> 00:02:55,272 These two waves are going to start overlapping, 87 00:02:55,272 --> 00:02:57,307 and where they overlap constructively, 88 00:02:57,307 --> 00:02:58,645 you'd get a bright spot, 89 00:02:58,645 --> 00:03:00,126 and where they overlap destructively, 90 00:03:00,126 --> 00:03:01,742 you'd get a dark spot. 91 00:03:01,742 --> 00:03:04,239 Where it's sort of half constructive, half destructive, 92 00:03:04,239 --> 00:03:07,432 you might get a mediumly bright spot. 93 00:03:07,432 --> 00:03:08,990 How do we figure out what's going to be? 94 00:03:08,990 --> 00:03:10,776 Well, I can't draw this precise enough 95 00:03:10,776 --> 00:03:13,021 to show you that, so let me get rid 96 00:03:13,021 --> 00:03:16,929 of all of this mess real quick, get rid of that. 97 00:03:16,929 --> 00:03:18,469 Out of the bottom hole, what would you get? 98 00:03:18,469 --> 00:03:22,781 You'd get this, a nice spherical pattern coming out of here. 99 00:03:22,781 --> 00:03:26,445 It might not exactly be the same intensity throughout here, 100 00:03:26,445 --> 00:03:29,858 but I can't draw it with the exact right intensity. 101 00:03:29,858 --> 00:03:31,559 Up here, this intensity of this portion 102 00:03:31,559 --> 00:03:33,985 would be smaller than this portion here, 103 00:03:33,985 --> 00:03:35,735 the degree to which it's spreading, 104 00:03:35,735 --> 00:03:37,481 but this will help me visualize it. 105 00:03:37,481 --> 00:03:39,722 You've got this wave spreading out, 106 00:03:39,722 --> 00:03:40,602 out of the bottom hole. 107 00:03:40,602 --> 00:03:43,311 You also have a wave spreading out of the top hole. 108 00:03:43,311 --> 00:03:44,450 Now these are going to overlap. 109 00:03:44,450 --> 00:03:46,094 Let's draw them both, boom. 110 00:03:46,094 --> 00:03:47,488 Waves overlapping. 111 00:03:47,488 --> 00:03:48,709 In the same region you're going to have 112 00:03:48,709 --> 00:03:50,934 constructive and destructive interference. 113 00:03:51,348 --> 00:03:54,983 If you look, remember, these lines represent peaks, 114 00:03:54,983 --> 00:03:59,427 so every time a peak lines up right over a peak, 115 00:03:59,427 --> 00:04:02,187 or in the middle, a valley over a valley, 116 00:04:02,187 --> 00:04:05,622 every time the wave is exactly in phase, 117 00:04:05,622 --> 00:04:06,945 when it gets to the same point, 118 00:04:06,945 --> 00:04:08,997 these are all constructive points, 119 00:04:08,997 --> 00:04:11,868 so right in the middle you'd get a big bright spot. 120 00:04:11,868 --> 00:04:13,261 That's kind of weird. 121 00:04:13,261 --> 00:04:15,498 Right in between these holes there'd be a big bright spot. 122 00:04:15,498 --> 00:04:16,278 Where else? 123 00:04:16,278 --> 00:04:17,591 Well, look at this. 124 00:04:17,591 --> 00:04:21,223 This is constructive, constructive, all constructive. 125 00:04:21,224 --> 00:04:23,142 They form a line, they get these lines 126 00:04:23,142 --> 00:04:25,993 of constructive interference. 127 00:04:25,993 --> 00:04:29,303 Same with this line, constructive, constructive, 128 00:04:29,303 --> 00:04:31,012 all the way over to here. 129 00:04:31,012 --> 00:04:34,033 So on the wall, you'd see multiple bright spots. 130 00:04:34,033 --> 00:04:36,294 Down here, these are all constructive 131 00:04:36,294 --> 00:04:38,658 because peaks are lining up perfectly. 132 00:04:39,811 --> 00:04:41,715 I'd get another one here. 133 00:04:41,715 --> 00:04:44,045 You'd keep getting these bright spots on the wall. 134 00:04:44,045 --> 00:04:45,654 They wouldn't last forever. 135 00:04:45,654 --> 00:04:48,063 At some point, it'd start to die off. 136 00:04:48,063 --> 00:04:49,933 It'd be hard to see, but you'd be getting 137 00:04:49,933 --> 00:04:52,393 these bright spots continuing on. 138 00:04:52,393 --> 00:04:55,116 At some point, they're so dim you can't see them. 139 00:04:55,116 --> 00:04:58,244 In the middle, well, wherever ... 140 00:04:58,244 --> 00:04:59,770 Let's see, what's a good point to look at? 141 00:04:59,770 --> 00:05:02,937 Wherever a peak lines up with a valley, 142 00:05:02,937 --> 00:05:04,971 so this wave's a peak right here, 143 00:05:04,971 --> 00:05:06,393 but for the other wave, lookit, 144 00:05:06,393 --> 00:05:08,661 we're in between the two green lines, 145 00:05:08,661 --> 00:05:11,134 so in that point you'll have destructive, 146 00:05:11,134 --> 00:05:13,407 because the peak is matching up with the valley. 147 00:05:13,608 --> 00:05:15,842 This would be destructive and this would be destructive, 148 00:05:15,842 --> 00:05:18,727 so in between here you get a destructive point. 149 00:05:19,050 --> 00:05:21,400 The same is true, in between each of these 150 00:05:21,400 --> 00:05:23,148 perfectly constructive points, 151 00:05:23,148 --> 00:05:25,217 you'd get a perfectly destructive point, 152 00:05:25,217 --> 00:05:27,779 and in between those it'd be kind of half constructive 153 00:05:27,779 --> 00:05:29,901 half destructive, would merge into each other, 154 00:05:29,901 --> 00:05:31,808 and what you'd get, sometimes physicists 155 00:05:31,808 --> 00:05:34,017 draw a little graph to represent this, 156 00:05:34,017 --> 00:05:36,019 you get a bright spot in the middle. 157 00:05:36,019 --> 00:05:37,367 This is sort of representing a graph 158 00:05:37,367 --> 00:05:41,877 of the intensity zero, and then another bright spot, 159 00:05:41,877 --> 00:05:44,337 and it goes down to zero again, another bright spot. 160 00:05:44,337 --> 00:05:45,805 They get weaker and weaker as you go out. 161 00:05:45,805 --> 00:05:47,396 At some point, it's hard to see. 162 00:05:48,035 --> 00:05:49,217 Same on this side. 163 00:05:49,217 --> 00:05:53,173 Zero, bright spot, zero, bright spot. 164 00:05:53,173 --> 00:05:56,084 This is the classic double slit pattern 165 00:05:56,084 --> 00:05:57,323 you'll see on the wall, 166 00:05:57,323 --> 00:06:01,467 and it's caused by wave interference in two dimensions. 167 00:06:01,874 --> 00:06:03,928 What's the rule for wave interference in two dimensions? 168 00:06:03,928 --> 00:06:07,144 The same rule as the wave interference for one dimension. 169 00:06:07,144 --> 00:06:08,165 It was this, remember. 170 00:06:08,165 --> 00:06:12,594 For one dimension, delta X, the path length difference 171 00:06:12,594 --> 00:06:16,464 had to be zero, lambda, two lambda, three lambda, 172 00:06:16,464 --> 00:06:19,973 so on, would give us constructive interference. 173 00:06:19,973 --> 00:06:21,454 Now, if you're paying close attention, 174 00:06:21,454 --> 00:06:24,054 you might say, "Hold on, there was a condition." 175 00:06:24,054 --> 00:06:26,543 Remember, this was only true if there was no 176 00:06:26,543 --> 00:06:30,338 funny switcheroo business with the back of the speaker. 177 00:06:30,338 --> 00:06:32,678 We had to make sure that these two sources 178 00:06:32,678 --> 00:06:34,769 were in phase to start off with. 179 00:06:34,769 --> 00:06:37,221 Is that true of these light waves? It is. 180 00:06:37,221 --> 00:06:40,750 In fact, that's why we do it double slit like this. 181 00:06:40,750 --> 00:06:43,559 That's why we take one wave, we let one wave 182 00:06:43,559 --> 00:06:45,235 come through here. 183 00:06:45,235 --> 00:06:47,459 That way, we break it up into two pieces. Why? 184 00:06:47,459 --> 00:06:50,559 Because we know if a peak was going into the top hole, 185 00:06:50,559 --> 00:06:52,998 well, the same wave was going into the bottom hole, 186 00:06:52,998 --> 00:06:54,030 that's also a peak. 187 00:06:54,030 --> 00:06:57,507 This is a tricky way, a quick, easy way 188 00:06:57,507 --> 00:06:59,815 to make sure your two sources coming out 189 00:06:59,815 --> 00:07:02,723 of these two holes are exactly in phase. 190 00:07:02,723 --> 00:07:04,945 You don't have to worry about any phase 191 00:07:04,945 --> 00:07:07,260 difference caused by the source. 192 00:07:07,260 --> 00:07:09,048 You just have to worry about a phase difference 193 00:07:09,048 --> 00:07:11,062 caused by the fact that these waves are going 194 00:07:11,062 --> 00:07:14,104 to travel different distances to different points. 195 00:07:14,104 --> 00:07:15,073 What do I mean by this? 196 00:07:15,073 --> 00:07:16,915 What does path length difference mean here? 197 00:07:17,363 --> 00:07:20,083 Well, if I look at it from this top line, 198 00:07:20,083 --> 00:07:22,506 or this top hole, this is basically like our speaker, 199 00:07:22,506 --> 00:07:23,918 one source here and one source here, 200 00:07:23,918 --> 00:07:26,252 but it's light instead of sound waves, 201 00:07:26,252 --> 00:07:29,639 from here to the center bright spot, 202 00:07:29,639 --> 00:07:31,410 the wave from the top hole had to travel 203 00:07:31,410 --> 00:07:34,035 a certain distance, and from the bottom hole 204 00:07:34,035 --> 00:07:37,240 to that spot, the wave had to travel a certain distance. 205 00:07:37,240 --> 00:07:41,872 Basically, this we can call X one, this length X two. 206 00:07:41,872 --> 00:07:45,963 The path length difference would be X one minus X two. 207 00:07:45,963 --> 00:07:47,515 The difference in these, and you can just made it 208 00:07:47,515 --> 00:07:48,928 the absolute value if you want, 209 00:07:48,928 --> 00:07:50,720 but the size of the difference between 210 00:07:50,720 --> 00:07:52,849 these two path lengths, what is that going to be? 211 00:07:52,849 --> 00:07:54,885 For right in the center, that one's 212 00:07:54,885 --> 00:07:56,911 just delta X equals zero, 213 00:07:56,911 --> 00:07:59,010 because the waves are traveling the same distance 214 00:07:59,010 --> 00:08:00,668 to get to that point. 215 00:08:01,185 --> 00:08:02,142 That makes sense. 216 00:08:02,142 --> 00:08:03,949 That's a constructive point because zero 217 00:08:03,949 --> 00:08:05,664 gives you a constructive point 218 00:08:05,664 --> 00:08:07,612 when the path length difference is zero. 219 00:08:07,612 --> 00:08:09,235 How about the next point? 220 00:08:10,177 --> 00:08:13,584 The wave from the bottom has to travel this far. 221 00:08:13,584 --> 00:08:16,176 The wave from the top hole has to travel this far. 222 00:08:16,176 --> 00:08:18,199 This time, they're not traveling the same distance. 223 00:08:18,199 --> 00:08:20,447 The wave from the bottom hole is traveling farther. 224 00:08:20,447 --> 00:08:21,774 How much farther? 225 00:08:22,101 --> 00:08:22,865 It's got to be the next one, 226 00:08:22,865 --> 00:08:24,414 it's got to be lambda. 227 00:08:24,414 --> 00:08:26,350 So this wave's going to be traveling-- 228 00:08:26,350 --> 00:08:29,217 the bottom wave would travel one wavelength further 229 00:08:29,217 --> 00:08:31,934 to get to this point than the wave from the top hole 230 00:08:32,549 --> 00:08:33,840 because that's the next possibility 231 00:08:33,840 --> 00:08:35,690 for constructive interference. 232 00:08:35,690 --> 00:08:40,690 Note, it's not from here to there that's one wavelength. 233 00:08:41,143 --> 00:08:42,700 This is a common misconception. 234 00:08:42,700 --> 00:08:45,773 This distance on the wall between constructive points 235 00:08:45,773 --> 00:08:47,790 is not one wavelength. 236 00:08:48,473 --> 00:08:50,873 The difference in path length that one wave 237 00:08:50,873 --> 00:08:52,891 travels to get there compared to the other wave 238 00:08:52,891 --> 00:08:54,133 is one wavelength. 239 00:08:54,133 --> 00:08:55,711 I bet you can guess the next one. 240 00:08:55,711 --> 00:08:58,981 The next one, delta X, would just be two wavelength, 241 00:08:58,981 --> 00:09:00,468 and you can keep going. 242 00:09:00,468 --> 00:09:01,908 How about the destructive points? 243 00:09:01,908 --> 00:09:03,212 Shoot, you know how to do that. 244 00:09:03,212 --> 00:09:04,611 These are going to be the half wavelengths, 245 00:09:04,611 --> 00:09:06,044 lambda over two. 246 00:09:06,044 --> 00:09:09,312 This one's going to be three lambda over two, 247 00:09:10,127 --> 00:09:11,036 and so on. 248 00:09:11,036 --> 00:09:12,510 Down here, what would you get? 249 00:09:12,510 --> 00:09:15,385 Well, if you got rid of the absolute value sign 250 00:09:15,385 --> 00:09:17,415 and you wanted to, you could start talking about 251 00:09:18,030 --> 00:09:20,963 this delta X would be negative one lambda. 252 00:09:21,446 --> 00:09:24,566 This one would be negative two lambda, and so on. 253 00:09:25,371 --> 00:09:27,179 You could have negative values if you wanted 254 00:09:27,179 --> 00:09:29,225 to note the fact that there might be lower 255 00:09:29,225 --> 00:09:31,433 or higher, depending on where you were 256 00:09:31,433 --> 00:00:00,000 in this interference pattern.